AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& \Delta AGB\sim \Delta BGC\\ & \frac{AB}{BC}=\frac{BG}{GC}=\frac{AG}{BG}\\ & \frac{12}{BC}=\frac{4\sqrt{5}}{GC}=\frac{8}{4\sqrt{5}}\\ & GC=10\\ & \frac{12}{BC}=\frac{4\sqrt{5}}{10}\\ & BC=6\sqrt{5}\end{array}$$